Electrolyte solutions are ubiquitous in chemical process industries. Current efforts in the development of activity coefficient-based electrolyte thermodynamic models largely follow two main tracks: 1) virial expansion empirical expressions represented by the Pitzer equation and 2) local composition semi-empirical expressions represented by the electrolyte NRTL model. See Pitzer, K. S., Thermodynamics of Electrolytes, I. Theoretical Basis and General Equations, J. Phys. Chem., 1973, 77, 268-277; Song, Y., Chen, C.-C., Symmetric Electrolyte Nonrandom Two-Liquid Activity Coefficient Model, Ind. Eng. Chem. Res., 2009, 48, 7788-7797; Chen, C.-C., Britt, H. I., Boston, J. F., Evans, L. B., Local Composition Model for Excess Gibbs Energy of Electrolyte Systems, Part I: Single Solvent, Single Completely Dissociated Electrolyte Systems, AIChE J., 1982, 28, 588-596; Chen, C.-C., Song, Y., Generalized Electrolyte NRTL Model for Mixed-Solvent Electrolyte Systems, AIChE J., 2004, 50, 1928-1941. These models provide sound thermodynamic frameworks to quantitatively correlate available thermodynamic data for interpolation and extrapolation.
More recently a segment-based electrolyte activity coefficient model has been proposed as a correlative and predictive thermodynamic framework. See Chen, C.-C., Song, Y., Extension of Non-Random Two-Liquid Segment Activity Coefficient Model for Electrolytes, Ind. Eng. Chem. Res., 2005, 44, 8909-8921; Song, Y., Chen, C.-C., Symmetric Nonrandom Two-Liquid Segment Activity Coefficient Model for Electrolytes, Ind. Eng. Chem. Res., 2009, 48, 5522-5529. The model requires component-specific “conceptual segment” parameters that can be determined from correlating experimental data in a few representative systems. The model can then be used to qualitatively predict phase behavior of any electrolyte systems as long as the conceptual segment parameters are known for the molecules and electrolytes.
COSMO-based activity coefficient models such as COSMO-SAC (Conductor-like screening model-segment activity coefficient) and COSMO-RS have been shown to be relatively successful predictive models for molecular systems. See Lin, S. T., Sandler, S. I., A Priori Phase Equilibrium Prediction from a Segment Contribution Solvation Model. Ind. Eng. Chem. Res., 2002, 41, 899-913; Mullins, E., Oldland, R., Liu, Y. A., Wang, S., Sandler, S. I., Chen, C.-C., Zwolak, M., Seavey, K. C., Sigma-Profile Database for Using COSMO-Based Thermodynamic Methods, Ind. Eng. Chem. Res., 2006, 45, 4389-4415; Klamt, A., COSMO-RS From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, Elsevier, Amsterdam, 2005. The COSMO-SAC solvation model uses the “screening charge density” or “sigma profile” of the molecular surface calculated from quantum chemistry as a descriptor to compute the activity coefficient of each component in mixtures. These models are capable of reasonably robust predictions for thermodynamic properties of thousands of components and their mixtures without any experimental data. See Wang, S, Sandler, S. I., Chen, C. C., Refinement of COSMO-SAC and the Applications, Ind. Eng. Chem. Res., 2007, 46, 7275-7288. Although COSMO-based models were originally developed for molecular systems, they were later successfully applied to molecular species in ionic liquids. See Klamt, A., COSMO-RS From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, Elsevier, Amsterdam, 2005; Wang, S, Thermodynamic Properties Predictions using the COSMO-SAC Solvation method, Ph.D. thesis, University of Delaware, 2007. The success suggests that the COSMO-SAC formulation provides adequate representation of short-range molecule-molecule interactions and, to a certain extent, the short-range molecule-ion interactions.
There is, however, a continuing need for improved predictive electrolyte thermodynamic models capable of an adequate representation for the short range ion-ion interactions.